We consider two sequences of orthogonal polynomials (Pn) n≥0 and (Qn) n≥0 with respect regular functionals u and v, respectively. We assume that), I is the identity operator, x defines a lattice, and △f (s) = f (s + 1) − f (s). We show that under some natural conditions, the functionals u and v are connected by a rational factor whenever m = k, and for k > m, u and S k−m x v are semiclassical functionals and in addition Sxu and S k−m+1 x v are connected by a rational factor. This leads to the notion of (M, N )-coherent pair of measures of order (m, k) extended to orthogonal polynomials on lattices.